# Question Video: Finding the Unknown Length in a Right Triangle Using Trigonometry Where the Unknown Is on the Top of the Fraction Mathematics • 11th Grade

Find đť‘Ą to two decimal places

01:35

### Video Transcript

Find đť‘Ą to two decimal places.

What do we notice about this image? First of all, we notice that itâ€™s a right triangle. Because itâ€™s a right triangle, we can use our trig ratios. Side length đť‘Ą is opposite the angle weâ€™re given and side length 12 is adjacent to the angle weâ€™re given.

Opposite over adjacent side lengths tell us that weâ€™re dealing with the tangent ratio. Tangent of 20 degrees is equal to the opposite side length đť‘Ą over the adjacent side length 12. Tangent of 20 degrees equals đť‘Ą over 12.

Weâ€™re solving for đť‘Ą. So we multiply the right side of our equation by 12. If we multiply the right side, we have to multiply the left side. 12 times the tangent of 20 degrees is equal the side length đť‘Ą. Using a calculator, we calculate the tangent of 20 degrees and then multiply that by 12. It gives us a decimal number that doesnâ€™t terminate.

We want to round this number to two decimal places. In the second decimal place, there is a six. We look to the right of that and we have a seven, which is greater than five. Our six in the hundredths place is rounded up to a seven. And everything to the left of the hundredths place stays the same.

Side length đť‘Ą is equal to 4.37.